SEEREVENUE ACADEMY
ENRICHMENT MATH CLASSES
FINANCIAL ANALYSIS / BUSINESS CONSULTING
Calculus AB
Students demonstrate knowledge of both the formal definition and the graphical interpretation of limit of values of
functions. This knowledge includes one-sided limits, infinite limits, and limits at infinity. Students know the definition of
convergence and divergence of a function as the domain variable approaches either a number or infinity.
1.1 Students prove and use theorems evaluating the limits of sums, products, quotients, and composition of functions.
1.2 Students use graphical calculators to verify and estimate limits.
1.3 Students prove and use special limits, such as the limits of (sin(x))/x and (1−cos(x))/x as x tends to 0.
2.0 Students demonstrate knowledge of both the formal definition and the graphical interpretation of continuity of a function.
3.0 Students demonstrate an understanding and the application of the intermediate value theorem and the extreme value
theorem.
4.1 Students demonstrate an understanding of the derivative of a function as the slope of the tangent line to the graph
of the function.
4.2 Students demonstrate an understanding of the interpretation of the derivative as an instantaneous rate of change.
Students can use derivatives to solve a variety of problems from physics, chemistry, economics, and so forth that
involve the rate of change of a function.
4.3 Students understand the relation between differentiability and continuity.
4.4 Students derive derivative formulas and use them to find the derivatives of algebraic, trigonometric, inverse
trigonometric, exponential, and logarithmic functions.
5.0 Students know the chain rule and its proof and applications to the calculation of the derivative of a variety of composite
functions.
6.0 Students find the derivatives of parametrically defined functions and use implicit differentiation in a wide variety of
problems in physics, chemistry, economics, and so forth.
7.0 Students compute derivatives of higher orders.
8.0 Students know and can apply Rolle’s Theorem, the mean value theorem, and L’Hôpital’s rule.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points,
and intervals in which the function is increasing and decreasing.
10.0 Students know Newton’s method for approximating the zeros of a function.
11.0 Students use differentiation to solve optimization (maximum-minimum problems) in a variety of pure and applied contexts.
12.0 Students use differentiation to solve related rate problems in a variety of pure and applied contexts.
13.0 Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate
integrals.
14.0 Students apply the definition of the integral to model problems in physics, economics, and so forth, obtaining results in
terms of integrals.
15.0 Students demonstrate knowledge and proof of the fundamental theorem of calculus and use it to interpret integrals as
antiderivatives.
16.0 Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of
revolution, length of a curve, and work.
17.0 Students compute, by hand, the integrals of a wide variety of functions by using techniques of integration, such as substitution, integration by parts, and trigonometric substitution. They can also combine these techniques when appropriate.
18.0 Students know the definitions and properties of inverse trigonometric functions and the expression of these functions as
indefinite integrals.
19.0 Students compute, by hand, the integrals of rational functions by combining the techniques in standard 17.0 with the
algebraic techniques of partial fractions and completing the square.
20.0 Students compute the integrals of trigonometric functions by using the techniques noted above.
21.0 Students understand the algorithms involved in Simpson’s rule and Newton’s method. They use calculators or computers
or both to approximate integrals numerically.
22.0 Students understand improper integrals as limits of definite integrals.
23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of
real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine
whether a series converges.
24.0 Students understand and can compute the radius (interval) of the convergence of power series.
25.0 Students differentiate and integrate the terms of a power series in order to form new series from known ones.
26.0 Students calculate Taylor polynomials and Taylor series of basic functions, including the remainder term.
27.0 Students know the techniques of solution of selected elementary differential equations and their applications to a wide
variety of situations, including growth-and-decay problems.
Pre-calculus
Interpret functions that arise in applications in terms of the context.
4. For a function that models a relationship between two quantities, interpret key features of graphs and
tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the
relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive,
or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it
describes. For example, if the function gives the number of person-hours it takes to assemble engines in
a factory, then the positive integers would be an appropriate domain for the function.
Analyze functions using different representations.
7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and
using technology for more complicated cases.
d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
10. (+) Demonstrate an understanding of functions and equations defined parametrically and graph
them. CA
11. (+) Graph polar coordinates and curves. Convert between polar and rectangular coordinate systems. CA
Build new functions from existing functions.
3. Identify the effect on the graph of replacing by , and for specific
values of (both positive and negative); find the value of given the graphs. Experiment with cases and
illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd
functions from their graphs and algebraic expressions for them.
4. Find inverse functions.
b. (+) Verify by composition that one function is the inverse of another.
c. (+) Read values of an inverse function from a graph or a table, given that the function has an inverse.
d. (+) Produce an invertible function from a non-invertible function by restricting the domain.
Perform arithmetic operations with complex numbers.
3. (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex
numbers.
Represent complex numbers and their operations on the complex plane.
4. (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and
imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.
5. (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically
on the complex plane; use properties of this representation for computation.
6. (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and
the midpoint of a segment as the average of the numbers at its endpoints.
Represent and model with vector quantities.
1. (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by
directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., )
2. (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
3. (+) Solve problems involving velocity and other quantities that can be represented by vectors.
Perform operations on vectors.
4. (+) Add and subtract vectors.
a. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their
sum.
c. Understand vector subtraction as , where is the additive inverse of , with the same
magnitude as and pointing in the opposite direction. Represent vector subtraction graphically by
connecting the tips in the appropriate order, and perform vector subtraction component-wise.
5. (+) Multiply a vector by a scalar.
a. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction;
perform scalar multiplication component-wise.
b. Compute the magnitude of a scalar multiple.
Perform operations on matrices and use matrices in applications.
6. (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in
a network.
7. (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are
doubled.
8. (+) Add, subtract, and multiply matrices of appropriate dimensions.
9. (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a
commutative operation, but still satisfies the associative and distributive properties.
10. (+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is non-zero if and only
if the matrix has a multiplicative inverse.
11. (+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
12. (+) Work with 2x2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
Interpret the structure of expressions.
1. Interpret expressions that represent a quantity in terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret as the product of and a factor not depending on .
2. Use the structure of an expression to identify ways to rewrite it.
Rewrite rational expressions.
6. Rewrite simple rational expressions in different forms; using inspection, long division, or, for the more complicated examples, a computer algebra system.
7. (+) Understand that rational expressions form a system analogous to the rational numbers, closed under
addition, subtraction, multiplication, and division by a non-zero rational expression; add, subtract, multiply, and divide rational expressions.
Solve systems of equations.
8. (+) Represent a system of linear equations as a single matrix equation in a vector variable.
9. (+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology
for matrices of dimension 3 x 3 or greater).
Mission Statement
If you reach to your goals constantly, a king will take your place! When your calendar is perfectly filled out, it's time for you to find a job!
the goal
methods of tackling complicated and tiring Math problems, small reasonable classes, convenience and attractive accessibility of our enrichment programs all will help you to go higher in knowledge and problem-solving skills.
business analysis opportunities
ABOUT US
Seerevenue Academy Since 2025
California Business License number 014711 Business Owner: Anahid H. Abadi Citizen of United States of America lives in Blackhawk California Religion: Shea B.Sc. , CIS 2001 MBA, Management Golden Gate University 2007 v MSc, Mathematics California State University East bay 2016 Other Websites: MY EYE FOOTSTEP CALENDARS (nonprofit) Since 2021 https://www.eyefootstep.com/